Theoretical and Experimental DNA Computation (Natural ...

3
Models of Molecular Computation
“... there’s a statue inside every block of stone.” – George Orwell,
Coming up for Air
3.1 Introduction
The purpose of this chapter is to describe several examples of the various
models of molecular computation that have been proposed in the literature.
Note that we have used the term “molecular” rather than the more specific
“DNA”, as we wish to abstract away from the (perhaps) intended biological
substrate for each model, and concentrate on the computational features of
the machine model.
We may describe abstract models of computation without necessarily considering
their implementation. In [64], for example, for the sake of emphasising
what is inherently parallelisable within problems, the authors disregard constraints
of implementation. However, the operation sets within the models
described here are constrained by the availability of various molecular manipulation
techniques. The implementation of abstract operations will largely
determine the success or failure of a model. Many of the models described in
this chapter use abstract operations common to the others, such as set union.
However, even though models may utilize similar operations (e.g., removal of
an element from a set), the chosen implementation method may differ from
model to model. Details may impact implementation in various ways:
1. The volume of DNA required (analogous to space in complexity theoretical
terms) to perform the computation may vary by exponential factors.
2. Each operation takes a certain amount of time to implement in the laboratory,
and so the sequence of operations performed determines the overall
time complexity of the algorithm. Thus, the techniques chosen have a
direct bearing on the efficiency of a DNA-based algorithm. In addition,